American Journal of Mechanical Engineering, 2013, Vol. 1, No. 1, 6-13

Available online at http://pubs.sciepub.com/ajme/1/1/2

DOI:10.12691/ajme-1-1-2

Comparison between Analytical Calculus and FEM for a

Mechanical Press Bed

Cătălin Iancu*

Engineering Faculty, University “Constantin Brâncuşi” of Târgu-Jiu, Romania

*Corresponding author: ciancu@utgjiu.ro

Received December 29, 2012; Revised January 16, 2013; Accepted February 26, 2013

Abstract In the first part of this paper is presented a method for calculating stress of press bed, based on

expansion of classic methodology, using reduced frame, determined by the points of application of force and the

gravity center line, thus determining sectional geometry and maximum stress. Calculus is extended considering cross

sections of the frame, from 15° to 15°, providing more information on both maximum values and the distribution of

these tensions. Values obtained confirm the assumption that using the simplified structure is obtained generally large,

the calculation usually used for verification. By this method one can get stresses in different sections, not only the

maximum value. For a complete stress value and their distribution require a more complex calculation, furthermore

allowing any dimensional optimization, such as FEM. Second, is presented a step-by-step method for modeling the

frame of mechanical press studied, using Pro/Engineer, in order to perform consequent static or dynamic analysis

based on FEM, using COSMOS/M. So are presented the stages of defining the mesh, the environment bonds, the

loads, and finally performing analysis and result interpretation. According to FEA results a continuous distribution

of displacements and stresses that validate the model. At the end are presented considerations and comparison

between the results of analytical method and FEM, regarding stress values and their distribution.

Keywords: CAD/FEA software, complex structures, mechanical press, modeling, FEM, stress distribution

1. Introduction

The press frame is a basic element of the press, aiming

to support all of the machine kinematics and force

transmission from the press to the work-piece. In this

paper is considered the frame for a crank press, one of the

most common types of such machines. Properly working

characteristics and for functional reasons, as specified in

OSHA 1910.217 [1], crank mechanical presses frames are

made in two models: half frames (open) and complete

frames (closed).

Open frames are distinguished by the shape of the

normal section made through the column, at table level,

and it can be assembled mono-block design or assembled

construction.

The column can have one or two uprights, second

version allowing through the opening between columns to

increase the workspace of the die, and easier parts and

waste disposal. Columns or pillars are secured by means

of ribs and some braces. Common variants of the cross

sections can be mentioned: closed contour, half contour,

open contours or cross-section profile of T. Frames after a

closed contour presses are used for fixed and the semi-

closed or open contours for both fixed press and for the

folding ones.

As specified in the Machine-tools, typification rules [2],

the materials used in performing frames are cast iron and

steel castings Fc 250...Fc 350 (Ft 25D…Ft 35D according

to NF-A 35-501-77) or OT (cast steel) class for cast

frames, and steel type OL 37, OL 42.2k, OL 44.2k and OL

52.2k (E 24-2, E 26-2, E 30-2 and E 36-2 according to

NF-A 35-501-77) for welded frames of plates.

The selection of construction materials is subject,

however, largely by pressing force. Thus, for forces

ranging from 63 kN…1600 kN can be used open frames

with two columns (pillars) reclining or tilt-bed, or open

frames with two columns fixed and folding table. Open

section frames with closed contour section are used in the

range of 63 kN...1600 kN, but can be used even for higher

nominal force. In the same limits size, closed frames are

approx. 15 % more rigid than open frameworks, the

decisive factor in choosing the technology and

construction of the frame being technical-economic

considerations.

2. Crank Mechanical Press Bed Calculus

For presses with capacities up to a nominal force of

5000 kN, such as universal or blanking presses, eccentric

or crank drive is still the most effective drive system [3].

Mechanical presses crank bearing pedestal calculation is

based on the determination of stresses and strains that

occur under full load, for the nominal pressing force.

In terms of static calculation performed, types of frames

for these presses are divided into three general categories

[4]:

1. Frame with a single upright, considered a straight

beam eccentric loaded, crank shaft being eccentric type

end, oriented transversely (perpendicular to the machine).

American Journal of Mechanical Engineering 7

2. Frame with a single upright, double, tilt usually,

regarded as a curved beam eccentric loaded, crank shaft

being oriented longitudinally (parallel to the machine).

3. Frame with two uprights, loaded symmetrically, for

closed presses, crank shaft being placed longitudinally or

transversely.

As Tabără et al. shown in [5], and Tschaetsch in [6] the

calculation considers a flat charging, concentrated forces

acting in the plane of symmetry of the bearing pedestal.

Following will be treated half frame bearing pedestal

(open), crank shaft being oriented longitudinally (parallel

to the machine). In this case, must determine the reduced

scheme framework, driven by the points of application of

force and the centers of gravity line, specific to sections of

the frame.

Figure 1. Reduced frame scheme

The reduced frame scheme in Figure 1 shows that in a

certain section A-A the bed is subject to a bending

moment, given by:

YFM

AANi (1)

where: FN A-A is the nominal deformation strength,

corresponding to calculation section, Y - distance from the

axis of force to the center of gravity calculation section.

Because along the beam represented by frame the

bending moment remains constant, cross-sectional area

considered is to be required for interior tensile and

compressive on the outside.

Resistance modules for the two parts of the section will

be considered:

3

3

[ ]

[ ]

zt

zc

IW m traction

m

IW m compression

b m

(2)

And the corresponding bending stresses:

2

2

/ int ( )

/ ext ( )

ii t

t

ii c

c

MN m traction

W

MN m compression

W

(3)

By overlapping with constant stress given by:

2/N A At

A A

FN m

A

(4)

Maximum tensions will arise to external fibers of

considered section:

2 2max max/ /t it t c ic tN m N m (5)

This calculation is presented through a numerical

example, as stated by Iancu [7] represented by a crank-

type press frame, type PMCR - 63 (Figure 2), mechanical

press with half frame type (open) tilt, adjustable stroke

and nominal force of 630 kN, crank shaft oriented

longitudinally.

The classic calculation is only for maximum force, on

its direction. This calculation is extended, as specified by

Iancu in [8], by considering all cross sections of the frame,

from 15° to 15°, which allows estimation of tensions after

several directions, providing information on both the

maximum values and the distribution of these tensions,

making sizing more accurate.

It also mentioned that for the calculation is made the

assumption that the tensile and compressive efforts and

deformations will be perpendicular to the direction A - A

up to G - G, the calculating sections. Scheme for

calculating the bed is shown in Figure 3. The frame is

made of sheet plates from OL 44.2k in welded

construction. According to the literature, wall thickness is

between 8 and 60 mm. Depending on similar machine

tools made worldwide and those clauses in terms of

characteristics, have settled the original dimensions from

structural and functional conditions, followed by

subsequent calculations, to finally check these dimensions.

Figure 2. PMCR 63 press

It also states that, due to the symmetry of the bearing

pedestal (of course, at this stage are not considered various

technological clippings) will be performed the calculation

for half the considered sections (see figure 4).

Sectional area is considered:

2A 135 180 0.0315t

m (6)

The position of the center of gravity of the section will

be:

8 American Journal of Mechanical Engineering

2135 300.1285

315

i i

t

A yy mG A

(7)

Moment of inertia of the composite section is

considered:

3

2

12

b hi iI A y

z i i

8 4121500 145800043014 29722 204361 10

12m

(8)

Resistance modules are:

6 3

11

2043616354.4 10

32.15

IzW m

z Yc

6 3

22

2043613532.6 10

57.85

IzW m

z Yc

(9)

For section A-A, which is perpendicular to the direction

of the force of the press, will be considered for calculating

the nominal power of the press, so:

630000F Nd (10)

Bending moment acting on the considered section will

be:

1

25 32.15 63000 57.15 180022.52 2

i

FdM Nm (11)

Tensile constant stress is:

7 2int

3150010 /

2 315

dt

t

FN m

A (12)

Tensile stress, i.e. compression stress, due to bending

loads will have values:

5 2int

1

1800225283 10 /

6356.4

it inc

MN m

Wz

(13)

5 2

2

1800225509 10 /

3532.6

ic ext

MN m

Wz

(14)

Maximum stress to outer fiber of the considered section

will be:

5 2int 100 283 383 10 /t N m

5 2100 509 409 10 /c ext N m (15)

B'

A'

A

B

C

D

EFG

H G FE

D

C

BAA'

B'

C'

D'E'F'G'H'

1 1 1

1

1

1

1

1

1

1

1

1

1111

C'

D'E'F'

G'

H G F EDCBAA'B'

F'G'H' D'

C'

E'

1

H'

T

Fd

Fd

0'0

T

Figure 3. Scheme for calculating the bed

Figure 4. Section A-A

Following this model, calculation is performed in other

sections of calculation considered B-B...G-G, determining

for each: area and center of gravity of the section, moment

of inertia and resistance modulus; force component acting

on the section considered, the maximum stress for

considering sections.

These elements are summarized in Table 1.

Table 1. Calculation elements for considering sections

Section Area m2

Moment of inertia

m4

Force N

int

N/m2 ext

N/m2

A-A 315·10-4 204361·10-8 630000 3.83·107 4.09·107

B-B 325.5·10-8 221737.7·10-8 608530 3.62·107 3.91·107

C-C 360.7·10-8 296109·10-8 545590 2.95·107 3.22·107

D-D 357.8·10-8 163222·10-8 445470 3.40·107 4.13·107

E-E 431.5·10-8 187022·10-8 315000 2.16·107 2.23·107

F-F 365.5·10-8 185803·10-8 163050 1.16·107 8.4·106

G-G 326·10-8 142904·10-8 - - -

As seen in Figure 5, which presents the distribution of

these stress, the highest values are obtained in section A-A

and section D-D, inclined at 45°, where, for a frame

incorrectly sized may appear cracks in welding or even in

basic material. Note that the absolute values of these

efforts are quite small compared with the allowable

material resistance, which shows that the frame is really

oversized.

Figure 5. Stress distribution on frame sections

3. Modeling Frame Strategy for FEA

3.1. General Elements

For the discretization of any structure must be selected

the most suitable finite elements, regarding the geometry,

the loads, the desired precision and many other conditions.

In the majority of cases the structure geometry

determines the finite element type to be used, as stated

Imbert in [9]. It is recommended using a single type of

American Journal of Mechanical Engineering 9

finite element, but for complex structures may be used two

or even more type of finite elements.

One-dimensional finite elements- are used when

geometry, material properties, etc. may be described by a

single space coordinate.

Bi-dimensional finite elements- are used when two

space coordinates may describe geometry, material

properties, etc.

Three-dimensional finite elements- are used when the

structure is massive and the geometry, material properties,

etc. may be described by three space coordinates. The

base element is a tetrahedron, but may be used other

shapes, like cuboids, prism, hexahedron.

At the same time the size of the elements is very

important in order to achieve correct result and the desired

precision. Regarding this aspect a compromise must be

made between the size and the number of elements

because increasing the number of elements leads to the

growth of the problem, and increase the solving time.

If the analyzed structure has no geometry

discontinuities, material properties and loads, can be

divided in finite elements approx. equals, and the node

distances will be uniform. The number of elements is

connected with the desired precision, but it is a certain

number of elements for that the relation precision-solving

time is optimized, as stated by Rao in [10].

3.2. Discretization Variants

As Neumann and Hahn stated in [11], the frames of

machines are generally complex structures, three-

dimensional, which requires a detailed analysis of variants

for modeling and discretization. Theoretically can be used

three possibilities of discretization, and thus obtaining

three model variants:

- beam type elements, which have the advantage of easy

modeling, a reduced solving time, but cannot accurate

modeling concentrators zones;

- plate type elements which have the advantage of a

detailed examination of local phenomena, but having a

bigger solving time;

- solid type elements (three-dimensional), which

models very exactly the whole structure, but having a

large saving time.

It’s also obvious that it can be combined various types

of elements, when necessary.

By analyzing the geometry of the structure it comes to

conclusion that can be discretized in majority with plate

type finite elements. How the majority of bed elements is

welded plates, it’s clear that plates can model structure.

The modeling is done on middle plane, regarding the

thickness of plates. The bedplates have been discretized

by SHELL elements with 3 nodes, the thickness of a plate

being constant. For the reason of real convey of forces, the

cantilevers and the bosses from the upper side have been

discretized by SOLID elements.

The version of “COSMOS/M” software [12] used for

solving, permit using three important classes of finite

elements:

- One-dimensional (BEAM class);

- Bi-dimensional (PLANE2D class);

- Three-dimensional (SOLID class).

So the "COSMOS/M" software permits any variant of

structure discretization, in order to achieve a model very

real and to obtain result accuracy, especially when

analyzing complex structures like a press bed.

3.3. Modeling and Processing the Bed Model

The solving time is main motivation in choosing a

discretization variant and complying software. The

appearance of a new solving technique (FFE - Fast Finite

Element) developed by Structural Research & Analysis

Corporation was decisive in using COSMOS/M [13].

For solving a problem of structural analysis and

optimization of a complex structure like a mechanical

press bed must be followed certain phases:

a- completing geometric model; b- establishing the

analysis type; c- defining the finite element type; d-

defining the mesh; e- defining material characteristics; f-

defining geometric characteristics.

a) Completing geometric model

First it must be realized a geometric model most

accurate of the bed, using a dedicated CAD software, or

even the geometric modeler of COSMOS/M. This

modeler is quite cumbersome, so was chosen dedicated

CAD software (it’s recommended a soft that can perform

parametric modeling and work integrated with FEA

software). Such a program is Pro/Engineer [14], produced

by American corporation Parametric Technology Corp.

The problems and phases of modeling are not detailed

here.

b) Establishing the analysis type

The load for such a structure is complex. Practically it

is a dynamic load and the natural frequencies are very

important. In this paper, will be presented the modeling

and only the static analysis of the structure, made mostly

for validating the geometric model.

c) Defining finite element type

After completing the geometric model, presented in

Figure 6, for subsequent FEA, it must be done the

meshing. It has been mentioned that the discretization can

be done using plate elements (SHELL 3), or solid

elements (TETRA 4). Since majority of the structure is

realized of welded plates of different thickness, between

10 - 80 mm, it will be used shell type elements for the

whole structure, and for the cantilevers and the bosses,

tetrahedron elements.

d) Defining the mesh

Using this type of finite elements it has been done the

discretization of the structure, obtaining the mesh

presented in Figure 7. The mesh was done directly in

Pro/Engineer, because importing geometry in

COSMOS/M and then creating the mesh in this software

have revealed a series of inconsistencies as a result of a

different precision of coordinates in the two programs. In

addition Pro/Engineer has special facilities of refining the

initial mesh.

e) Defining material characteristics

The refined mesh presented in Figure 7 has been

imported in COSMOS/M, in this stage the compatibility

being complete. For defining material measurement it has

been used the SI system material library of software,

existing the possibility of defining every property at row,

measurement units according to the SI system material

library of software, existing the possibility of defining

every property at row, measurement units according to the

SI system.

10 American Journal of Mechanical Engineering

The bed is made of OL 44.2k, and the table is made of

OL 52.2k, STAS 500/2-80. The material chosen from a

library is STEEL (plain steel), which has the usual

characteristics of this material.

f) Defining geometric characteristics

The geometric characteristics refer to this type of

structure the thickness of every plate. When importing the

mesh in COSMOS/M for FEA have been defined finite

element groups, and also the thickness and FE type adjoin

to every real constant (the initial thickness of every plate

of the bed).

Figure 6. Geometric model of the press bed

Figure 7. Refined mesh

4. Static Analysis of PMCR-63

Mechanical Press Frame

The model of the complex structure analyzed,

completed and prepared as shown before, is now ready for

finite element analysis. For FEA analysis, either static or

dynamic, in COSMOS/M must be followed the phases:

defining the mesh, defining the environment bonds,

defining the loads, performing analysis and result

interpretation.

4.1. Defining the Mesh

The mode of obtaining the mesh was presented before.

The mesh has 10307 nodes, 25734 finite elements and

103590 degrees of freedom (DOF), element type SHELL

3 for discretization of all bed plates and type TETRA 4 for

discretization of cantilevers and the bosses (Figure 8).

4.2. Defining the Environment Bonds

The bed structure may be studied in half, regarding the

symmetry in plane YOZ. This symmetry regards the

geometry, the loads and the environments bonds. However,

for more accurate evaluation of the model was chosen the

modeling of the whole structure. The environment bonds

apply to nodes being in the zone of the bed resting on the

foundation. In this zone are blocked all DOF (3

translations and 3 rotation). In Figure 9 are presented the

environment bonds.

Figure 8. The discretized structure

4.3. Defining the Loads

Defining the loads of analyzed structure can be

approached in many points of view:

- defining real loads (shock type, on short time, with

hard to estimate damping), in this case is needed a detailed

dynamic analysis;

- defining static loads, like a cutoff impairment of loads

to static domain, when this is real enough.

The forces developped for on working are generated by

rod-crank mechanism. Their effect is transmitted by

American Journal of Mechanical Engineering 11

superior bosses and by the bed table in the whole structure.

Therefore, on the bed action:

- action forces on bed table, with maximum value of 63

tf;

- reaction forces on the upper bosses, same value, but

contrasted direction.

Figure 9. The environment bonds

Since the action of these forces doesn’t concentrate, the

forces on upper bosses were considered like a uniform

distributed pressure on bosses’ width, having the value:

p1=630000/(4x25x100)=63·106N/m2 (16)

And the force on bed table like a distributed pressure on

circular surface of 300 mm diameter:

p2=630000x4/(3002 -502) = 9.17·106 N/m2 (17)

In Figure 10 and Figure 11 are shown these pressures.

To these loads is added the weight of the structure,

considered by an automated option in the software.

Figure 10. Pressure on bosses

4.4. Performing Analysis and Result

Interpretation

The model prepared for analysis as shown, was studied

with COSMOS/M, with solving option FFE (Fast Finite

Element). The results show both displacement and stress,

concerning maximum values and distribution. In Figure

12 is presented the stress distribution, by Von Misses

theory.

Figure 11. Pressure on bed table

Figure 12. Von Misses stress distribution, Von

, N/m2

The admissible strengths considered are: bending

strength 2·E+08 N/m2 and traction-compression strength

1.8 ·E+08 N/m2.

It can be noticed that stress values are generally low

compared with traction-compression strength of bed

material, Von = 1.8 E+08 N/m2, higher values being

recorded only locally, in the bed table zone. The

maximum stress is 1.82 ·E+08 N/m2, and because the

structure is stressed on traction-compression compound

with bending, the admissible strength considered is

Vonmax = 2·E+08 N/m

2, so the stress is below the

admissible strength.

12 American Journal of Mechanical Engineering

5. Conclusions

This calculation presents a novelty compared with

classical calculus because are considered different sections

of the frame, from 15° to 15°, which allows estimation of

stresses after several directions, providing more

information on both maximum values and the distribution

stresses.

For a more accurate and complete stress values and

their distribution is clearly required a more complex

calculation, which allows eventually a dimensional

optimization, considering real dynamic load, such as FEM,

as stated by Neumann in [15].

Figure 13. Von Misses stress corresponding to section A-A, Von

, N/m2

Figure 14. Von Misses stress corresponding to section D-D, Von

, N/m2

So in the second part of the paper are presented the

stages needed for modeling complex structures, such as a

mechanical press bed, shown by a numeric example and

also the preparing of the model for subsequent FEA

analysis.

It has to be mentioned that the specialty literature is

relatively poor in offering complex stress calculus on

models realized in majority using SHELL elements, for

plates made structures.

Based on FEA application the results show a

continuous distribution of displacements and stresses that

validate the model, proving it correct. It can be noticed

that stress values are generally low compared with

traction-compression strength of bed material, higher

values being recorded only locally.

The maximum stress is 1.82 ·E+08 N/m2, and because

the structure is stressed on traction-compression

compound with bending, the admissible strength

considered is Von max = 2·E+08 N/m2, so the stress is

really below the admissible strength.

In Figure 13 and Figure 14 are presented the stress

values obtained by FEA in section A-A, respectively D-D.

In Table 2 is presented the comparison between the values

obtained by classical calculus and by FEA.

Table 2. Comparison between classical calculus and by FEA

Section Area

m2

Force

N

Classical

calculus

int

N/m2

Classical

calculus

ext

N/m2

FEA

Von

max N/m2

A-A 315·10-4 630000 3.83·107 4.09·107 < 3·107

D-D 357.8·10-8 445470 3.40·107 4.13·107 < 3.2·107

It can be noticed that stress values obtained by classical

calculus are higher than the values obtained by FEA,

confirming the assumption that using only a calculation

based on the simplified structure, leads to an oversized

structure, the calculation method being usually used for

verification.

Also, with this type of analysis it became possible

knowing values in every point of the bed that interests,

and preparing the way for the sizing optimization of such

a complex structure, optimization considering dynamic

load too.

References

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platen presses, USA, 1991.

[2] I.C.P.M.U.A., Sibiu Subsidiary, Machine tools, typification rules,

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[3] Schuler Inc., Metal forming handbook, Springer, Germany, 1998,

33-44.

[4] Smith, D.A., Mechanical press types and nomenclature, MI, USA, 2005, 1-27.

[5] Tabără, V., Catrina, D. and Ghana, V., Calculus, design and adjustment of presses, Technical Publishing House, Bucureşti,

Romania, 1976, 71-80.

[6] Tschaetsch, H., Metal forming practice, Springer, Germany, 2005,

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Pitesti, Romania, 2002, 20-39, 160-190.

[9] Imbert, J.F., Analyse de structure par elements finis, Ecole

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[10] Rao, S.S., The finite element method in engineering, fifth edition,

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American Journal of Mechanical Engineering 13

[11] Neumann, M., and Hahn, H., “Computer simulation and dynamic

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[12] Cosmos/M -Finite Element Analysis System, User Guide, Structural Research & Analysis Corp., Los Angeles, CA, USA,

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[14] Pro/Engineer -User guide, Parametric Technology Corporation, Waltham, MA, USA, 2001.

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